论文标题
扭曲托里的拓扑T偶二。
Topological T-Duality for Twisted Tori
论文作者
论文摘要
我们将由于Mathai和Rosenberg引起的拓扑T二维的$ C^*$ - 代数形式主义，以及一系列的拓扑空间，其中包括带有二元性曲折的弦理论压缩中的圆环捆绑包，例如Nilmanifolds，以及许多其他示例。我们在此设置中开发了一个简单的过程，用于构建从交换性$ c^*$ - 代数开始的T-Duals，其操作为$ {\ Mathbb r}^n $。我们详细介绍了任意维度的几乎Abelian Solvmanifolds的一般类别，在其中，我们根据纯粹的理论数据为存在经典的T偶会提供了必要和足够的标准，并将其作为与非客体dixmier-dixmier-douady类别的连续性trace代数明确计算。我们证明，任何这样的solvmanifold都有$ c^*$ - 代数捆绑的非交通式Tori给出的拓扑T偶，我们也明确地对其进行了计算。原始圆环束的单构成成为纤维代数之间的莫里塔等效性，因此这些$ c^*$ - 代数严格描述了非几何字符串理论的t折。
We apply the $C^*$-algebraic formalism of topological T-duality due to Mathai and Rosenberg to a broad class of topological spaces that include the torus bundles appearing in string theory compactifications with duality twists, such as nilmanifolds, as well as many other examples. We develop a simple procedure in this setting for constructing the T-duals starting from a commutative $C^*$-algebra with an action of ${\mathbb R}^n$. We treat the general class of almost abelian solvmanifolds in arbitrary dimension in detail, where we provide necessary and sufficient criteria for the existence of classical T-duals in terms of purely group theoretic data, and compute them explicitly as continuous-trace algebras with non-trivial Dixmier-Douady classes. We prove that any such solvmanifold has a topological T-dual given by a $C^*$-algebra bundle of noncommutative tori, which we also compute explicitly. The monodromy of the original torus bundle becomes a Morita equivalence among the fiber algebras, so that these $C^*$-algebras rigorously describe the T-folds from non-geometric string theory.
